Paired, Total, and Connected Domination on the Queen’s Graph Revisited
نویسندگان
چکیده
منابع مشابه
Total domination versus paired domination
A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γt. The maximal size of an inclusionwise minimal total dominating set, the upper total domination num...
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The domination number γ(G), the independent domination number ι(G), the connected domination number γc(G), and the paired domination number γp(G) of a graph G (without isolated vertices, if necessary) are related by the simple inequalities γ(G) ≤ ι(G), γ(G) ≤ γc(G), and γ(G) ≤ γp(G). Very little is known about the graphs that satisfy one of these inequalities with equality. I.E. Zverovich and V...
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A subset S of V is called a total dominating set if every vertex in V is adjacent to some vertex in S. The total domination number γt (G) of G is the minimum cardinality taken over all total dominating sets of G. A dominating set is called a connected dominating set if the induced subgraph 〈S〉 is connected. The connected domination number γc(G) of G is the minimum cardinality taken over all min...
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An outer-connected dominating set for an arbitrary graph G is a set D̃ ⊆ V such that D̃ is a dominating set and the induced subgraph G[V \ D̃] be connected. In this paper, we focus on the outerconnected domination number of the product of graphs. We investigate the existence of outer-connected dominating set in lexicographic product and Corona of two arbitrary graphs, and we present upper bounds f...
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Let / be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an /-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an /-dominating set is denned to be the /-domination number, denoted by 7/(G). In a similar way one can define the connected and total /-domination numbers 7 C| /(G) and...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2016
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2016.61001